MATHEMATICS AND STATISTICS

by Dr. Richard Nowakowski

This event is held every second year, participation is by invitation only and is limited. Experts and graduate students from around the world are invited to mix with the local graduate students. There are no lectures. The topic is combinatorial games, such as Chess, Checkers and Go. We agree on three problems in advance and the group works on whichever they find the most appealing after everyone arrives.

Eighteen months ago, Thane Plambeck and then Aaron Siegel and Thane had major breakthroughs in evaluating impartial, misere games. Certainly, one topic will be an attempt to extend these techniques to partisan misere games.

Meghan Allen (Dal), JP Grossman (NY), Alan Hill (Dal), Richard Nowakowski (Dal), Paul Ottaway (Dal), Thane Plambeck (Calif.) Aaron Siegel (Princeton), Angela Siegel (Dal), Fraser Stewart (Dal), David Wolf (Gus. Adolp. Coll.), and possibly Elwyn Berlekamp ( Berkeley ). Regrets: Michael Albert (NZ).

Highlights from the past: Games-At-Dal 3 resulted in two groundbreaking papers. One by JP Grossman and Aaron Siegel, Reduced Canonical Form, showed a concept postulated in 1993 was, in fact, well defined and they gave an evaluation procedure. The other paper Spittles by G. A. Mesdal, a non-de-plume for the 12 participants, made headway on a game introduced in the 19 century. The game of Clobber was invented during Games-At-Dal 2, two papers resulted and a world championship was held at an International Conference at Dagstuhl the following year. Games-At-Dal 1 also resulted in two papers and gave thesis topics to two MSc students.

by Dr. Joanna Mills Flemming

A workshop entitled "Spatial/temporal modeling for marine ecological systems" was held August 17-19, 2005 here at Dalhousie University . This workshop was sponsored by the National Program on Complex Data Structures (NPCDS) and was a first step towards a full proposal to NPCDS for funding to continue research on the workshop theme. In January of 2006, organizers Michael Dowd, Joanna Mills Flemming, Chris Field and Rick Routledge (SFU) were informed that this proposal had been successful. Financial support for graduate students and postdoctoral researchers is now in place for the next three years.

The workshop brought together researchers in statistics and marine ecology interested in the development of models for the analysis of complex temporal/spatial data. These data include, for example, animal tracking data as well as time series of biological variables from ocean observing systems. Keynote speakers included David Brillinger ( University of California , Berkeley ), Yvette Spitz ( Oregon State University ), Arnaud Doucet (UBC), Hans Ruedi Kuensch (ETH, Zurich ), Pierre Lermusiaux ( Harvard University ) and Ransom Myers ( Dalhousie University ). There were over 70 attendees.

by Dr. Richard Nowakowski

Cyber attacks have become increasingly severe, and current network security solutions offer only local protection from known cyber attacks. Graphs are an abstraction for a wide range of physical systems such as networks and searching graphs is a basic problem. Researchers have suggested and investigated several models. The important three considerations have are:

1: the amount of information---in the Cops-and-Robber model, which is characterized by perfect information, the Cops try to apprehend a Robber
and everyone knows everybody’s position at all times;

2: the speed of the protagonists---in the Searching model, which allows the intruder to have infinite speed, the searchers try to decontaminate a network after a biological or chemical spill;

3: whether the intruders multiply---in the Firefighting model, the fire or virus is observed to breakout and then propagates at finite speed, the object is to quarantine the outbreak.

The Workshop will be in two sessions, Cops-and Robber models in the morning and Searching and Firefighting in the afternoon. The 15 min talks will consist of a review of a topic---the important definitions, main models and typical questions, results and any conjectures. Presenting proofs is not required and actively discouraged unless there is a good reason. Brainstorming will follow the reviews. As the presentations continue, the idea is to obtain more linkages and cross-fertilization between the models.

Session 1: Cops and Robber models

11am : Sable McKeil, Cops and Robber on graphs with unreliable edges.

11:15 : Alan Hill, Cops and Robbers with differential speeds.

11:30 : Nancy Clarke, Technology, cops and robbers.

11:45 : General Discussions

12:30: Lunch

Session 2: Other models

1pm : Margaret-Ellen Messinger: firefighting.

1:15 : Richard Nowakowski, Cleaning as a model for searching.

1:30 : Richard Nowakowski, Watchman problems.

1:45 : Discussions

by Dr. C.C.A. Sastri and S. Sikka

The Dalhousie-CMS math camp has now become an annual tradition. It was held for the first time in the summer of 2000 and has been repeated every summer since then. Thus it is in its seventh year now. Last year it was held from the 4 th to the 8 th of July; this year, the dates are July 17-21. It is held under the auspices of the Canadian Mathematical Society (CMS) and Dalhousie University , with financial support from various sources, including Dalhousie, ESSO, and NSERC/PromoScience. The organizers, from the beginning, have been Chelluri C.A. Sastri and Suraj Sikka.

The camp is aimed at high school students in Nova Scotia . The purpose is to identify, stimulate, and encourage mathematical talent. Accordingly, letters calling for nominations are sent out in early March to all the high schools in the province, both public and private. The stipulation is that a school can make no more than two nominations and that the nominees are to have finished either Grade 10 or Grade 11. Last year, the response from the public schools, while slightly better than the previous year’s, was still down from earlier years. It was, however, sufficient to provide a good pool of students from which to make the selection. The response from the private schools was poor, as before. Altogether, there were 31 applicants. We are trying different ways of attracting more good students: For the last few years Dalhousie has been running two outreach programs, "Nova Scotia Math League" and "Math Circles." Richard Hoshino, a graduate student here and a mainstay of the CMS math camp – he was too busy with his thesis last year to participate in the camp – initiated both of them. He put a lot of work into those programs and established good connections with high school students and teachers in the province. Paul Ottaway, a graduate student, and Dr. Richard Nowakowski, are continuing the programs initiated by Richard. We hope and expect that, in the coming years, the work they are doing will generate greater interest in the camp among high school students in Nova Scotia .

In the selection process last year, we encountered a problem we had faced before: One of the criteria we have used for acceptance into the camp is performance on the Cayley/Fermat contests held by the University of Waterloo . However, it is becoming increasingly difficult to do so since many schools are not participating in these contests for financial reasons. This makes the task of selection harder, for the contests provide a uniform measure of excellence. The other criteria we use, such as grades and letters of reference, are useful but have the disadvantage of considerable variability. Equity of distribution in terms of gender as well as geographical location was also an important consideration. In the end, ten boys and ten girls representing almost all the regions in the province were selected.

The format of the camp was essentially the same as in previous years. All the instructors were faculty members at either Dalhousie or St. Mary's. Nobody, among the instructors, organizers or helpers, of whom there were many, received any payment for services rendered. However, all of them were invited to a thank-you dinner or lunch, depending upon their convenience.

The students arrived, and registered, on Sunday, July 3, between 1:00 and 2:30 pm . The organizers and the two chaperones, Sunita Gupta, and Paul Sheridan, received them. Paul is a graduate student in our department, and Sunita a high school mathematics teacher. Sunita worked as a chaperone before, but it was the first time for Paul. The students and the chaperones all stayed at Howe Hall, a student residence. They got along quite well. The students, in their comments after the camp, described their interaction with the chaperones in very positive terms.

Following registration, a reception was held for the students and their parents.

Computers were an integral part of the camp. The computer lab belonging to the Faculty of Engineering and located in the Dunn Building was placed at our disposal for the entire duration of the camp. For this we are grateful to the Engineering Faculty and, in particular, to Reg Peters, who is in charge of the lab. It was used to teach Maple, geometry, and statistical simulation. In addition, one of the instructors, Robert Dawson, taught the students how to print on their T shirts some of the work they had done in class. For this purpose, each of the students was given a T-shirt. They thoroughly enjoyed this activity, and the individualized T-shirts look beautiful.

Each day of the camp was divided into a morning session ( 9:00 to 12:00 , with a twenty-minute snack break) and an afternoon one ( 1:30 to 3:30 , with a ten minute break); please see the enclosed schedule for details. Each session consisted of a lesson. The lessons were not just lectures; there was plenty of interaction, problem solving and hands-on work. Since this format had worked well in previous years, we decided to follow it last year also. The consensus was that the camp went very well.

We are grateful to Ron Fitzgerald of MathResources Inc. for donating packages of their Math Dictionary. We believe the students were pleased to get them.

There were several extra-curricular activities—bowling, chess, a pizza party, etc. However, there were a couple of changes from those announced in the program: We could not schedule a visit to Shakespeare by the Sea as we did in previous years because of a conflict in the timetable; a presentation by an honors student in our department concerning the transition from high school to university had to be cancelled because of some last-minute problems. Also, we took the students to the Metro Center on Wednesday to see the Nova Scotia Tattoo. Since the price of admission ($20 per person) was higher than the amount budgeted ($10 per head) the students paid the difference. (We had asked the students and their parents at registration time whether this would be acceptable, and they all agreed. We were prepared to subsidize any students who couldn’t afford to pay the difference, but didn’t have to.) Every day, after the academic sessions were over, the students spent about an hour and a half playing sports or working out at Dalplex, the university’s athletics and sports complex.

There was a pizza lunch after the closing ceremonies on Friday July 8 th. Afterwards, the students were picked up by their parents.

Both Dalhousie and the CMS supported the camp. The CMS, with support from ESSO, NSERC/Promo Science and perhaps other sources, contributed $3000.00. Dalhousie supported the camp in many ways: $3000.00 from the President’s Office, $2000.00 from the Office of the Dean of Science; free use of the classrooms and the computer lab; free secretarial help, photocopying and miscellaneous items and services from the department; and free faculty time. We received enthusiastic help and support from our colleagues in organizing the camp and are grateful for it. A registration fee of $50 per student was charged except in cases of financial exigency.

In closing, it is our pleasant duty to thank all the instructors, without whose hard work and dedication the camp would not have been possible. We are also pleased to thank Gretchen Smith, the departmental administrator, and the secretaries, Maria Fe Elder, Paula Flemming, and Jackie Harnish-Grandy, for their unstinting help.
by Dr. R.P. Gupta

The fourteenth mathematics camp for black students was held in the second week of July 2005. The camp was organized by the Department of Mathematics and Statistics and the Black Educators Association of Nova Scotia. Thirty-two students were selected to attend the camp from schools all over Nova Scotia .

The aim of the camp is to generate interest in mathematics, statistics, computers and sciences so these students can pursue further studies with enthusiasm and appreciation of these subjects. The students are generally of grade six and seven, they are brought to the Dalhousie campus and stay in Howe Hall. Mornings and early afternoons are devoted to lectures and mathematical, statistical and computer activities, while late afternoon and evenings are devoted to extra curricular activities where they can apply the talents they have learnt in the classes and practice them.

They are taken to Dalplex for one hour each afternoon where they participate in swimming and play other games like basketball, tennis, etc. They also visited the Nova Scotia museum of history and science as well as the Discovery Centre. Students of the Camp also spent one evening at the Black Cultural Centre in Dartmouth where they were told about the mathematicians and scientists of black origin and a film was shown. The students were taught and cared for by six instructors (three university professors and three school teachers) and five chaperons. The Camp was organized under the direcrorship of Professor R.P.Gupta of Dalhousie University and Mr.Gerry Clarke of the Black Educators Association. It was financially supported by NSERC Promo Science Grant, Dalhousie University and the BEA.

by Drs. Tony Thompson, Renzo Piccinini, Summer School Directors

The fourth Atlantic Association for the Mathematical Sciences (AARMS) summer school took place at Dalhousie University from Sunday, July 17 to Saturday August 13, 2005 . As usual, four courses were offered. These were:Convexity and Fixed Point Algorithms in Hilbert Space. This was taught by Heinz Bauschke of the University of Guelph (he has since moved to the University of British Columbia at Kelowna ).

Integral Geometry of Convex Bodies and Polyhedra. This was taught by Daniel Klain of the University of Massachusetts at Lowell .

The Mathematics of Finance. This was taught by Wolfgang Runggaldier of the University of Padova , Italy .

Mathematical Statistics. This was taught by Bruce Smith of Dalhousie University .

The students came from a wide variety of places and, consequently, had a wide variety of backgrounds. In total there were 39 students from outside Dalhousie and 4 of our own students. Eight different countries were represented by the student body.

There were a number of social activities in connection with the summer school. There was a reception on the first Sunday evening at which we all (students, instructors and directors) met for the first time. We were glad to have the Director of AARMS and the Vice-President Academic of Dalhousie also at that reception. The next day there was a pizza lunch partially funded by the Canadian Math Society Undergraduate Student Committee. In the middle of the programme there was an organized bus trip to Lunenburg with a dinner that was partially funded by Clearwater Fine Foods.

Judging from the reactions of students and instructors, the summer school was successful and an enjoyable experience for everyone. Certainly, I found it extremely stimulating to have such a keen and active group of students on campus for the month.

Following that successful programme we are quite excited about the line-up of courses and instructors for this coming summer.

As usual, there will be four, beginning-graduate-level courses. These are: Elliptic Curve Cryptography given by Mark Bauer of the University of Calgary ; Massive Networks and Internet Mathematics given by Anthony Bonato from Wilfrid Laurier University ; Introduction to Algebraic Geometry given by Rick Miranda from Colorado State University ; and Introduction to Wavelet Theory and Numerical Applications given by Anita Tabacco from Politecnico di Torino.

Most of the students have now been selected and, again, it looks like a very interesting and exciting group of international students.

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